In many cases, a real-valued signal x(t) may be associated with a complex-valued signal a(t)e ~°(t) , the analytic signal associated with x'(t) with the characteristic properties x(t) = a(t) cos O(t) and "H(a(.)cos0(-))(t) = a(t)sin0(t). Using such obtained amplitude-frequency modulation the instantaneous frequency of x(t) at the time to may be defined to be 0'(t0), provided O'(to) >_ O. The pr...

We use the concept of the algebra eigenstates that provides a unified description of the generalized coherent states (belonging to different sets) and of the intelligent states associated with a dynamical symmetry group. The formalism is applied to the two-photon algebra and the corresponding algebra eigenstates are studied by using the Fock-Bargmann analytic representation. This formalism yiel...

The objective of the present work is to propose a method to automatically detect polarity of the speech signals by estimating instants of significant excitation of the vocaltract and the cosine phase of the analytic signal representation. The phase changes in the analytic signal around the Hilbert envelope (HE) peaks are found to vary according to the polarity of the given speech signal. The re...

Kernel learning is the problem of determining the best kernel (either from a dictionary of fixed kernels, or from a smooth space of kernel representations) for a given task. In this paper, we describe a new approach to kernel learning that establishes connections between the Fourier-analytic representation of kernels arising out of Bochner’s theorem and a specific kind of feed-forward network u...

We study generalizations of the sequence of the n-anacci constants that are constructed from the ratio limits generated by linear recurrences of an arbitrary order n with equal integer weights m. We derive the analytic representation of the class C of these ratio limits and prove that, for a fixed m, the ratio limits form a strictly

Morphological features are used to estimate the state of a random pattern (set) governed by a multivariate probability distribution. The feature vector is composed of granulometric moments and pattern estimation involves feature-based estimation of the parameter vector governing the random set. Under such circumstances, the joint density of the features and parameters is a generalized function ...

The estimation of the local phase and local amplitude of 1-D signals can be realized by the construction of the analytic signal. This includes the evaluation of the signal’s Hilbert transform, which performs a phase shift. In the past, different definitions of the analytic signal of multidimensional signals have been proposed, all of which are based on different combinations of partial and tota...

A simple, semi-analytic representation is developed for nuclear burning in Type Ia supernovae in the special case where turbulent eddies completely disrupt the flame. The speed and width of the “distributed” flame front are derived. For the conditions considered, the burning front can be considered as a turbulent flame brush composed of corrugated sheets of well-mixed flames. These flames are a...

The frequency estimate for a real sinusoid provided by the periodogram has a bias which is particularly severe for a short observation interval. In this paper, two improvements to the periodogram are proposed to reduce this bias. The rst method transforms the real tone to an analytic signal while the second algorithm subtracts the negative spectral line from the received signal, prior to applyi...

Bounds on the volume fraction of the constituents in a two-component mixture are derived from measurements of the effective complex permittivity of the mixture, using the analyticity of the effective property. First-order inverse bounds for general anisotropic materials, as well as second-order bounds for isotropic mixtures, are obtained. By exploiting an analytic representation of the effectiv...